Local derivation on the $n$-th Schr{\"o}dinger algebra

TL;DR

This paper proves that all local derivations on the $n$-th Schr{"o}dinger algebra are actually derivations, establishing a key structural property of these algebras.

Contribution

It demonstrates that every local derivation on the $n$-th Schr{"o}dinger algebra is a derivation, confirming a conjecture for this class of algebras.

Findings

All local derivations on $ $-th Schr{"o}dinger algebra are derivations.

The result extends understanding of derivation structures in Schr{"o}dinger algebras.

Provides a foundation for further algebraic analysis of Schr{"o}dinger algebras.

Abstract

This paper is devoted to study local derivations on the $n$-th Schr{\"o}dinger algebra $\mathcal{S}_{n}.$ We prove that every local derivation on $\mathcal{S}_{n}$ is a derivation.